Table Of ContentCFD M
ODULE
Turbulent Flow Modeling
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CFD M
ODULE
Turbulent Flow Modeling
Mehrzad Tabatabaian, PhD, PEng
MERCURY LEARNING AND INFORMATION
Dulles, Virginia
Boston, Massachusetts
New Delhi
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Copyright ©2015 by MERCURY LEARNING AND INFORMATION LLC. All rights reserved.
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MERCURY LEARNING AND INFORMATION
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M. Tabatabaian. CFD Module: Turbulent Flow Modeling
ISBN: 978-1-937585-43-3
Generated images were made using COMSOL Multiphysics® and are provided courtesy of
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To my wife
for her support, patience, and encouragement
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CONTENTS
Preface ix
Chapter 1 Turbulence Fundamentals:
A Summary 1
Overview 1
Some Observations of Turbulent Flows 2
Turbulence Characteristics 7
Turbulent Flow Types 12
Exercises 13
Chapter 2 Turbulence Modeling:
Approaches and Models 15
Overview 15
Modeling Methods 17
RANS Equations 19
Closure Methods 25
Specific RANS Models 27
First order models 27
Algebraic zero-equation models 28
One-equation model 29
Two-equation model 29
Second order models 30
Reynolds stress model 30
Algebraic stress model 30
COMSOL RANS Models 32
Overview and governing equations 32
Exact turbulent kinetic energy transport equation 33
Exact turbulent kinetic energy dissipation transport equation 38
k- model 40
k- model 46
Shear stress transport k- model 51
Wall Functions 56
Low-Re k- model 62
Sparlat-Allmaras model 66
Boundary and Initial Conditions 69
Algebraic yPlus model 70
L-VEL model 71
General Guideline for Turbulent Models Applications 72
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viii (cid:129) Contents
Chapter 3 COMSOL Multiphysics®:
Overview and CFD Module 75
Overview 75
Application Builder 78
COMSOL Modules 79
COMSOL Model/ Application Libraries and Tutorials 80
COMSOL Interface or Desktop 81
CFD Module 85
Example 3.1: Laminar flow in a sudden pipe contraction 87
Using Application Builder for Example 3.1 97
General Guideline for Building a Model in COMSOL 101
Exercises 102
Chapter 4 Turbulent Flow Models:
Application Examples 103
Overview 103
Example 4.1: Modeling of turbulent flow for an asymmetric diffuser 104
Example 4.2: Modeling of turbulent flow around the S809 airfoil 115
Example 4.3: Modeling of turbulent flow in a pipe with 90º bend 129
Example 4.4: Modeling of turbulent flow in a ventilated room 142
Example 4.5: Modeling of turbulent flow for a jet in cross-flow 157
Example 4.6: Modeling of turbulent flow over a
circuit board in a duct 168
Exercises 174
Appendix: Derivation of Governing Equations 177
Averaging Relations 177
Reynolds Averaged Navier-Stokes Equations (RANS) 179
Exact Equations for Reynolds Stress Transport 181
Mean-Kinetic Energy Equation 184
Exact Equation for Turbulent Kinetic Energy Transport 185
Exact Equation for Turbulent Kinetic Energy Dissipation Transport 187
Reynolds Averaged Equation for a Scalar Transport 189
References 191
Index 199
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PREFACE
Advances in computational methods, software tools and computer
power have made engineering and scientific computations more
available and economically viable in recent decades. Modeling has
become a mainstream, if not a necessary, step in engineering analy-
sis and design of products, processes, and systems. However, the
vast and powerful facilities available in current and modern com-
putational software packages do not sufficiently match the required
training that engineering and science students often receive. There-
fore, they may not have all the background training required to use
software packages. This has created a challenge for industry, to have
trained professionals who can create “reliable” models and fully uti-
lize commercially available software packages. On the other hand,
students, engineers, and scientists may not have the luxury of time
and training to learn all the necessary technical subjects like phys-
ics, mathematical modeling, numerical methods, and programming
languages. One of these challenging topics is turbulence modeling.
In industry, there is increasingly a pressing need for fluid flow com-
putations that involve turbulence modeling. This book aims to help
fill the gap on the topic of turbulence modeling in general, as well
as applications of COMSOL®- a commercially multiphysics software
tool with turbulence modeling facilities.
This book is written for practitioners in scientific and engineer-
ing fields e.g., fluid mechanics, biomechanics, and other related
fields, as well as students in engineering. The main objective of the
material is to introduce the fundamental physics, characteristics,
and common models of turbulent flows for practical and industry
applications using COMSOL. Industrial and engineering discussion
questions and examples are presented with their solutions that could
serve as a guide for modeling similar or more complicated turbulent
flow problems.
Turbulent flows are complex; hence reliable and “accurate”
models are challenging, and in many cases, require parameters
that are specific to each problem and relevant to its boundary and
initial conditions. Developing comprehensive models for industrial
and practical applications has been a subject of research and devel-
opment since Boussinesq [1], who proposed the concept of eddy
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